Local deformation theory of algebraic schemes

Abstract: Deformation theory is the study of variations of structure of a given object, which can be used to study the original object. It can also be regarded as local geometry of a moduli space, if it exists. In this talk, I will introduce (local) deformation theory, using the formalism of functor of artin rings and discuss automorphism-deformation-obstruction vector spaces and how these are realized as certain cohomologies. Along the way, I will give examples of application to concrete cases, including deformations of schemes, closed subschemes, nonsingular varieties, quasi-coherent sheaves.